CHAOS THEORY

A modern development in mathematics and science that provides a framework for understanding irregular or erratic fluctuations in nature. Chaotic systems are found in many fields of science and engineering. Evidence of chaos occurs in models and experiments describing convection and mixing in fluids, in wave motion, in oscillating chemical reactions, and in electrical currents in semiconductors. It is also found in the dynamics of animal populations and attempts are being made to apply chaotic dynamics in the social sciences, such as the study of business cycles. A chaotic system is defined as one that shows "sensitivity to initial conditions." That is, any uncertainty in the initial state of the given system, no matter how small, will lead to rapidly growing errors in any effort to predict its future behavior. This "sensitivity to initial conditions" will make any long-term prediction of such phenomenon virtually impossible in reality. In other words, the system is chaotic and as such its behavior can be predicted only if the initial conditions are known to an infinite degree of accuracy, which is impossible. The possibility of chaos in a natural, or deterministic, system was first envisaged by the French mathematician Henri Poincare in the late 19th century. More recently, predictions have been made that the transition to chaotic turbulence in a moving fluid would take place at a well-defined critical value of the fluid's velocity (or some other important factor controlling the fluid's behavior). The term chaotic dynamics refers only to the evolution of a system in time. Chaotic systems, however, also often display spatial disorder: for example, in complicated fluid flows.